California Rep. Jeff Denham, one of the House Republicans warmest to an immigration overhaul, will announce his support for a House Democratic comprehensive reform bill – becoming the first GOP lawmaker to do so.

In an interview on Univision’s “Al Punto” set to air Sunday, Denham called the Democratic legislation unveiled earlier this month a “good solution” and said he was encouraging – and expecting – other like-minded House Republicans to come on board with the bill.

“The most important part of this is, this is a hot issue,” Denham said, according to an English-language translation of the interview. Denham spoke in Spanish. “We need to make sure that we have the entire country focused on this debate, so the more Republicans and Democrats we can come together on this, it’ll increase our chances of getting a full bill passed in the House.”

The Democratic proposal is primarily a tool to pressure Republican lawmakers such as Denham – who is one of the top electoral targets for House Democrats — to sign on to a legislative reform bill. House Republican leaders have publicly expressed a desire to take up immigration reform on the floor, but there is no official timetable and a shrinking window of time before lawmakers are again consumed with fiscal issues and the 2014 campaign season begins in earnest.

The legislation is mostly a carbon copy of the Senate Gang of Eight bill that passed with 68 votes, including 14 Republicans, in June. But it subtracts a dramatic buildup in border security, such as a doubling of agents along the U.S.-Mexico boundary, that has become controversial with many House Democrats and some House Republicans. It adds in its place a bipartisan border-security bill that has passed the House Homeland Security Committee.

Denham noted that revision as one of the factors that attracted him toward the House Democratic bill, as well as provisions that would allow a pathway to citizenship for undocumented immigrants who enlist in the U.S. military. The bill currently has support from 185 House Democrats.

Denham said he has a commitment from leadership for full hearings and floor time for immigration legislation in “the next month or so.”

“I’m confident he’s going to bring it to the floor,” Denham said, referring to Speaker John Boehner (R-Ohio). “But we’re going to continue to make sure that the entire country focuses on this, and that we actually get more Republicans that are willing to take a stand and get out there.”